Guichard
In any event, the FARs are dispositive on the issue: "Where it is doubtful that an operation is for “compensation or hire”, the test applied is whether the carriage by air is merely incidental to the person's other business or is, in itself, a major enterprise for profit." See definition of commercial operator, http://www.ecfr.gov/cgi-bin/text-idx?rgn=div8&node=14:1.0.1....
At Oral Argument, the FAA agreed the common law definition of common carriage applied.
See, https://soundcloud.com/flytenow/judge-wilkins-on-whether-the....
Despite this, the court did not apply the common law definition. Indeed, they ignored the question, "we therefore do not consider Flytenow’s argument that the FAA’s decision contravenes the common law."
So, the determination is that Flytenow pilots are engaged in common carriage, yet the central element of common carriage - commercial enterprise for profit - was not addressed by the Court.
Your last statement [Flying is dangerous and should not be subject to the race to the bottom and rent-seeking behavior that is the "sharing economy"] cuts against your own argument. There is no "rent-seeking" behavior where there is no possibility for profit. That's the whole point of the common carriage analysis, and why the FAA and the Court got it wrong.